Chapter Test
Sign In
Find the perimeter and the apothem. Then substitute their values in the formula A= 12aP to find the area of the regular polygon. After that you can use the formula for the volume of a prism.
2577.3m^3
To calculate the volume of a prism, we multiply the height of the prism and the area of its base.
We are given the height of the prism. Thus, we need first to find the area of the base. Note that the base is a regular hexagon.
The area of a regular polygon is half the product of its apothem and perimeter. Notice that we are only given the side length.
We will begin by finding the perimeter and the apothem of the polygon. Then we will use the formula A= 12aP to find the area, where P represents the perimeter and a represents the apothem.
6* 8= 48m The perimeter of the given polygon is 48 meters.
Let's now find the apothem. To do so, we will start by drawing the radii of the hexagon. Notice that the radii divide a regular hexagon into six congruent isosceles triangles.
Since corresponding angles of congruent figures are congruent, the vertex angles of the isosceles triangles formed by the radii are congruent. Moreover, since a full turn measures 360^(∘), we can divide 360^(∘) by 6 to obtain their measures. 360^(∘)/6=60^(∘) The vertex angles of the isosceles triangles measure 60^(∘) each.
The apothem bisects both the vertex angle of the isosceles triangle and its opposite side, which is a side of the hexagon. As a result, a 30^(∘)-60^(∘)-90^(∘) triangle is created. The length of its shorter leg is 8÷ 2=4m.
In this type of special triangle the length of the longer leg, which is the apothem, is sqrt(3) times the length of the shorter leg. Longer Leg: sqrt(3)* 4=4sqrt(3)m Therefore, the length of the apothem is 4sqrt(3) meters.
a= 4sqrt(3), P= 48
Multiply
1/b* a = a/b
Calculate quotient
B= 96sqrt(3), h= 15.5
Multiply
Use a calculator
Round to 1 decimal place(s)